Relaxation and microstructurein a model for finite crystal plasticity with one slip system in three dimensions

Sergio Conti; Georg Dolzmann; Carolin Kreisbeck

doi:10.3934/dcdss.2013.6.1

Article Contents

2013, Volume 6, Issue 1: 1-16. Doi: 10.3934/dcdss.2013.6.1

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Relaxation and microstructure in a model for finite crystal plasticity with one slip system in three dimensions

1.
Institut für Angewandte Mathematik, Universität Bonn, Endenicher Allee 60，53115 Bonn
2.
Fakultät für Mathematik, Universität Regensburg, 93040 Regensburg
3.
Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213

Received: April 30, 2011

Revised: June 30, 2011

Published: January 2013

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Abstract

Modern theories in crystal plasticity are based on a multiplicative decomposition of the deformation gradient into an elastic and a plastic part. The free energy of the associated variational problems is given by the sum of an elastic and a plastic energy. For a model with one slip system in a three-dimensional setting it is shown that the relaxation of the model with rigid elasticity can be approximated in the sense of $\Gamma$-convergence by models with finite elastic energy and diverging elastic constants.

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Mathematics Subject Classification: Primary: 49J45; Secondary: 74C15.

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